Solve the simultaneous equation by elimination: 3x + y = 11 and 5x + y = 4

Simultaneous equations have at least two unknowns that must have the same value in each equation. This means the value of x and y in both equations must be the same. To solve this by elimination, the aim is to first remove one of the unknowns and then calculate the other. In this case, variable y has the same coefficient of 1 in both equations so it can be "eliminated" by subtracting the two equations. The trick is to subtract each term: 3x - 5x = -2x; y - y = 0; 11- 4 = 7 Hence, we're left with: -2x = 7. By dividing both sides of the equation by -2, we can see that x = -3.5. Now we can find the value for y using any of the equations. Using the first equation, if we plug in x = -3.5, we have -10.5 + y = 11; by adding 10.5 to both sides of the equation, we get y = 21.5. To cross-check the answer, plug in the value of x (-3.5) and y (21.5) to both equations to ensure you get 11 and 4 respectively. If you don't, you've made a mistake somewhere along the line. x = -3.5 and y = 21.5 are the unique solutions to these equations.